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I propose an alternative method for measuring the $CP$ violating phase$\phi_2$ ($\alpha$) without ambiguity in an extended SU(2) isospin triangleanalysis, which can ultimately be achieved by exploiting interference effectsbetween $B^0 \to \rho^0 \rho^0$ and $B^0 \to a_1^\pm \pi^\mp$ in atime-dependent flavour-tagged amplitude analysis. Under certain assumptions onthe effective $\phi_2$ in each channel, I demonstrate with an idealisedamplitude model that potential deviations in the measured $\phi_2$ due topenguin contamination in $B^0 \to a_1^\pm \pi^\mp$ are sufficiently largewithin current experimental uncertainties that this programme could be executedwith Run 3 data at LHCb and easily at Belle II.

Resolving the $\phi_2$ ($\alpha$) ambiguity in $B \to \rho \rho$